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Difference between revisions of "Center"

From Online Dictionary of Crystallography

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of the [[group homomorphism|homomorphism]] mapping an element ''a'' of ''G'' to the [[automorphism|inner automorphism]] ''f<sub>a</sub>'': ''g'' &rarr; ''aga<sup>-1</sup>''.  
 
of the [[group homomorphism|homomorphism]] mapping an element ''a'' of ''G'' to the [[automorphism|inner automorphism]] ''f<sub>a</sub>'': ''g'' &rarr; ''aga<sup>-1</sup>''.  
  
 
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==See also==
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*[[Centralizer]]
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*[[Normalizer]]
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*[[Stabilizer]]
  
  
 
[[Category:Fundamental crystallography]]
 
[[Category:Fundamental crystallography]]

Revision as of 13:59, 27 August 2014

Centre (Fr); Zentrum (Ge); Centro (Sp); Centro (It); 中心 (Ja).


The center (or centre) of a group G is the set Z(G) = { a in G : a*g = g*a for all g in G } of elements commuting with all elements of G. The center is an Abelian group.

The center of a group G is always a normal subgroup of G, namely the kernel of the homomorphism mapping an element a of G to the inner automorphism fa: gaga-1.

See also